(6x^2+4x-4)-(4x^2+3x+3)=

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Solution for (6x^2+4x-4)-(4x^2+3x+3)= equation:


Simplifying
(6x2 + 4x + -4) + -1(4x2 + 3x + 3) = 0

Reorder the terms:
(-4 + 4x + 6x2) + -1(4x2 + 3x + 3) = 0

Remove parenthesis around (-4 + 4x + 6x2)
-4 + 4x + 6x2 + -1(4x2 + 3x + 3) = 0

Reorder the terms:
-4 + 4x + 6x2 + -1(3 + 3x + 4x2) = 0
-4 + 4x + 6x2 + (3 * -1 + 3x * -1 + 4x2 * -1) = 0
-4 + 4x + 6x2 + (-3 + -3x + -4x2) = 0

Reorder the terms:
-4 + -3 + 4x + -3x + 6x2 + -4x2 = 0

Combine like terms: -4 + -3 = -7
-7 + 4x + -3x + 6x2 + -4x2 = 0

Combine like terms: 4x + -3x = 1x
-7 + 1x + 6x2 + -4x2 = 0

Combine like terms: 6x2 + -4x2 = 2x2
-7 + 1x + 2x2 = 0

Solving
-7 + 1x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 0.5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 0.5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 0.5x + x2 = 0 + 3.5
0.5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
0.5x + x2 = 3.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.5 + 0.0625

Combine like terms: 3.5 + 0.0625 = 3.5625
0.0625 + 0.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.887458609 and -1.887458609.

Subproblem 1

x + 0.25 = 1.887458609 Simplifying x + 0.25 = 1.887458609 Reorder the terms: 0.25 + x = 1.887458609 Solving 0.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.887458609 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.887458609 + -0.25 x = 1.887458609 + -0.25 Combine like terms: 1.887458609 + -0.25 = 1.637458609 x = 1.637458609 Simplifying x = 1.637458609

Subproblem 2

x + 0.25 = -1.887458609 Simplifying x + 0.25 = -1.887458609 Reorder the terms: 0.25 + x = -1.887458609 Solving 0.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.887458609 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.887458609 + -0.25 x = -1.887458609 + -0.25 Combine like terms: -1.887458609 + -0.25 = -2.137458609 x = -2.137458609 Simplifying x = -2.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.637458609, -2.137458609}

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